Title:
Ultraviolet Properties of N = 8 Supergravity at Five Loops

Abstract: We use the recently developed generalized double-copy construction to obtain
an improved representation of the five-loop four-point integrand of $N = 8$
supergravity whose leading ultraviolet behavior we analyze using state of the
art loop-integral expansion and reduction methods. We find that the five-loop
critical dimension where ultraviolet divergences first occur is $D_c=24/5$,
corresponding to a $D^8 R^4$ counterterm. This ultraviolet behavior stands in
contrast to the cases of four-dimensional $N = 4$ supergravity at three loops
and $N = 5$ supergravity at four loops whose improved ultraviolet behavior
demonstrates enhanced cancellations beyond implications from standard-symmetry
considerations. We express this $D_c=24/5$ divergence in terms of two
relatively simple positive-definite integrals reminiscent of vacuum integrals,
excluding any additional ultraviolet cancellations at this loop-order. We note
nontrivial relations between the integrals describing this leading ultraviolet
behavior and integrals describing lower-loop behavior. This observation
suggests not only a path towards greatly simplifying future calculations at
higher loops, but may even allow us to directly investigate ultraviolet
behavior in terms of simplified integrals, avoiding the construction of
complete integrands.